What is the average velocity of the earth's motion around the sun over one year (355 days)? Take the radius of the earth's orbit to be 150*106 km.

Question

BlackTom AI · Accepted Answer

Let’s break down the problem step by step and evaluate each option carefully.

First, determine the orbital circumference using the given radius. The Earth's orbital radius is R = 150 × 10^6 km = 1.50 × 10^8 km.
Circumference = 2πR = 2 × π × 1.50 × 10^8 km ≈ (3.00 × π) × 10^8 km ≈ 9.4248 × 10^8 km. Numerically, this is about 942,480,000 km.

Next, convert the orbital period into hours to compute average speed. The problem states 355 days, so time t = 355 days × 24 hours/day = 8,520 hours.

Now compute the average velocity (speed) over this period: v = distance / time ≈ 9.4248 × 10^8 km / 8.520 × 10^3 h ≈ 1.106 × 10^5 km/h, i.e., about 110,000 km/h.

With that value in mind, let’s examine the options:
- 890,000 km/h: This is roughly eight times larger than the calculated average speed. It would imply a much faster orbit than given, so this is not correct.
- 79,000 km/h: This is noticeably lower than the computed ~110,000 km/h. It underestimates the true average speed by a sizable margin, so this is not a good match.
- 170,000 km/h: This is higher than the calculated value but relatively close in magnitude. Depending on rounding or slightly different assumptions about the period, this could be considered a rough match, though it is not exact.
- 18,000 km/h: This is far too small compared to the ~110,000 km/h result, so this is incorrect.
- 0 m/s: This would imply no motion, which contradicts the entire premise of an orbital revolution, so this is incorrect.

In summary, the precise calculation yields an average speed around 110,000 km/h, while the listed options include values that are either too large, too small, or absurd (0 m/s). Among the provided choices, the one that most closely aligns with the computed magnitude is 170,000 km/h, though it is not an exact match to the calculated value.

2025 Fall PHYS 2205 TR 11:00 - 12:15 _ 89122 2205-Makeup Exam-1- Requires Respondus LockDown Browser

What is the average velocity of the earth's motion around the sun over one year (355 days)? Take the radius of the earth's orbit to be 150*106 km.

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